Friday, December 4, 2015

First semester review of Art of Problem Solving PreAlgebra Online course

I think one of the hardest things to decide on is a math curriculum when homeschooling, especially when hitting the middle school years. In our homeschool, middle school starts in the 5th grade, or when a child reaches PreAlgebra. For us that was this year with my then nine year old, Speedster. This is going to be an in-depth review of the first semester of the Art of Problem Solving online Prealgebra course.

Speedster has always been a "mathy" kid. I have tried to choose challenging programs for him, but never really found the right "fit" until we got to 4th grade last year. The combination of CTC Math and Beast Academy was good for him. It was the first time he really had to think about what he was doing in his math work. He worked through Beast Academy 4A - 4D and CTC Math 5th and 6th grade. Beast Academy did not have the 5th grade series ready for this school year, so we decided to make the leap to Art of Problem Solving PreAlgebra.

Let me start by saying the book is huge and even a little intimidating. The book itself is over 500 pages (not including the separate solutions manual), and lots of words. That can be a bit intimating for a severe dyslexic, even a profoundly gifted one. But, I knew the time was right for him to begin this program. My husband and I talked and decided to enroll him in the online program and purchase a copy of the online text as well.

I cannot say how happy I am with that decision. First, we definitely needed the text copy of the book. Speedster participates in a math circle and they use this textbook as their guide, so I am not disappointed with the purchase of the text. That said, the online version of the text is amazing! There are a couple of reasons why I truly love the online version of the book. The first is because the videos that are aligned with each chapter of the text are embedded in the book. So, no searching through video files and wondering if you are watching the correct one, the video that you need for an additional explanation is right there waiting for you. Second is that practice problems located in the book can be answered in the online text. Once you answer the question (and only after you answer the question) you can click, "take me to the solution" and you will be able to immediately compare your answer to the solution(s) provided.

Okay, enough about the book, now on to the actual online class. I believe all classes are offered in the evenings. This is because many students that take these courses are traditionally schooled students looking for additional challenge or preparing for math competitions. Class sizes are relatively large for an online program, Speedster's class has around 25 students. However, class size is never an issue.

The first component is the live session. The live session runs 1 1/4 hours (for us the class is 6:30 PM - 7:45 PM) one night a week. This was a bit tough on Speedster at first as he wasn't used to having an academic class so late in the day, but he learned to manage the time quickly. The live sessions have a lead teacher as well as teaching assistants. Teaching assistants are there to help students with questions in real time. For instance, the lead teacher will ask a question. Answers do not appear automatically on the screen. All students submit answers and only some of those that provided the correct answer will come on the screen. Those who did not provide a correct answer or who seem to be struggling a bit will have a private window that opens where the teaching assistant will help to guide them through the concept. This is brilliant as it ensures students who need help receive it and there is no shame associated with needing a bit more guidance. Because answers are put on the screen quickly, it also encourages students to answer fast when they can - so they can see their name on the screen. While there is no grade or points associated with getting your name on the screen, I have seen it be a motivator for my son to really pay close attention in class and try to be ready to answer questions.

Transcripts are provided for each online session, so if a student misses a session for some reason, they can read the transcript and be caught up with the rest of the class. It is also nice for students to be able to look back through the transcript if they need a refresher on something that was covered in class, or maybe misunderstood. It is nice to be able to go back through examples that were worked in class as they sometimes come up in the homework.

Let me talk a bit about names on the screen. Another great aspect of the online course is that real names are not used. So, the child is allowed to maintain their privacy, plus have a bit of fun with their name. My son chose to keep his online persona of Speedster and his name fit right in with the other names of students in the course.

The largest chunk of work comes from the "homework" associated with the course. In addition to the questions answered in the chapter sections preparing for class, students are provided with two other types of homework - Challenge Problems and Alcumus Problems.

Challenge Problems are just that, those problems that push a little beyond the concepts covered in the text. They are the same type of problem, but they require the student to extrapolate the concept just beyond what was covered in class. Most problems are word problems, which push the student to apply mathematical concepts learned in the text. These problems are graded automatically. How it works is the student will work out the problem and provide their answer, the right answer and solution for working out the problem will not appear until the correct answer is provided. However, there is a "Give up" button that can be pushed when the student feels they have reached their limit and they need to see the problem worked out. I love that the solution is not provided until the correct answer is provided because Speedster has found on several occasions that he took a longer way of answering the problem than was needed. This course is teaching him beautifully to become a more efficient and proficient problem solver. He is learning that it isn't just about getting the right answer, but "how" you get the right answer is important as well. He is also learning that their are often several efficient and correct ways of getting the answer. This isn't a cookie cutter approach to solving problems, this course is all about teaching mathematical thinking.

After about the 2nd or 3rd week of first semester, a writing problem is also required each week as part of the Challenge Problems. These problems require that the student not only answer the question, but explain their answer. These written problems are graded by a real, live person and feedback is robust. The student is given both a technical and stylistic grade. I have found the grades to be very tough, but very, very fair. The graders are very proficient in using the "sandwich" version of feedback. They first acknowledge what the student did correct, then discuss what was incorrect or incomplete, then finish with appropriate praise and encouragement. This is needed because the written problems go beyond anything I have ever seen in a math course, especially one with such young students (Speedster is not the only 5th grader in the course, there are many). For instance, Speedster is slowly learning to think beyond just the "right" answer the pops into his head. Often times the written questions ask students to explore "all possibilities" for a concept. One of the first lessons Speedster learned was to not forget about negative numbers when coming up with possible answers. Another great lesson learned was having ideas about concepts that were just on outside the edge of being correct. For instance, he once answered with a solution that would be correct in "most" instances, but there were some rare instances in which his solution would not be correct. Although they were times he probably wouldn't encounter for the next several years of mathematics, he learned that there are going to be some concepts in the future for which is assumption would be wrong. I love that he is being pushed to think outside of the silos of the math course he is currently in and to be reminded that mathematics concepts build upon one another, speak to each other, inform each other. He is learning the beauty in numbers. The second grade is a stylistic grade, it is based on using proper grammar and mathematics notations. Again, I love this! He is seeing that his grammar lessons do, in fact, have an impact in other areas and if he does want to truly become an aerospace engineer/black hawk pilot/wildlife researcher - he needs to write well just as much as he needs to know mathematics deeply. All hail the cosmos for getting confirmation that scientific minds still need the social sciences!

The second component of homework is Alcumus, which is an adaptive program that covers a more traditional scope and sequence of problems. One thing you will learn about the Art of Problem Solving is that it doesn't look or perform like traditional math courses. You cover things in a sequence that may feel unfamiliar. Also, there is going to be some assumption of proficiency in some topics or students will need to work on some of the more basic math functions outside of what is covered in the text. Behold, Alcumus! Alcumus is wonderful because it adapts to the skill level of the student. It basically assumes a level of proficiency, but if a student gets the problem wrong, it will automatically go back a level and let the student "catch up". However, this is done without it being obvious for the student. There is a colored bar that shows the student where they are in the concept. Red means the concept is unexplored, orange means they are working on the concept, green means they are proficient enough to move on to something new. If they want, they can continue to work and to blue, which means they have mastered the concept. This program is great and really squelched any fear of "gaps" with having such a young student jump to pre algebra in 5th grade for me.

This online program has been a great fit for Speedster. Now, when it comes to reviews there is often times a component of recommendation. So, the question is - would I recommend the Art of Problem Solving online course? The answer is, it depends. This course is amazing for a very specific type of student. The student must be both great in math and also really enjoy math. If a student that was great in math, but didn't enjoy math and enjoy struggling with math to get the correct answer - this course would be a disaster. A perfectionist that always has to be 100% "right" is not going to fare well, because it is really close to impossible to get 100% on the written problems, mainly because they are introducing the student to concepts that it is assumed are well beyond their current level of knowledge. On the reverse side, if a child enjoys math, but isn't great (not good, great) - they can also get discouraged. This class is asking students to again do things that are just beyond what they should be capable of. This class is designed to challenge students that are already exceptional math students. This isn't a class to "teach" pre algebra, this is a class designed to teach the theoretical framework that defines the rules in which preAlgebra operates. This isn't a class of "how" or even "what", it is a class of "why". If your child really needs to spend a significant time on the "how" of things like dividing negative fractions that include exponents, it may be a bit much to ask them to also uncover the theoretical rules driving the why behind that concept as well. The class also moves quickly, so if your child needs a lot of time to digest concepts, the online course may not be a good fit. The book self paced may be excellent, but the course itself moves online with the assumption that the student is moving along with it.  However, if you have a mathy kid that you just haven't been able to keep challenge and you know they want and need more - this is the course for you! Well worth every dollar spent.


  1. Very helpful. :) Thank for you sharing such a detailed review. We have the book and have begun working through it at home using the book, the resource videos, and Alcumus, but it sounds like my son would still really benefit from the challenge and mentoring the class offers. Also, I'm guessing they would be able to expect and evaluate the written problems from him more easily than I would -- something that I think would be great practice for him.

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